WASHINGTON (Reuters) - The European Commission is working on an idea of a budget for the 19 countries sharing the euro currency that could support investment and also serve as an unemployment re-insurance plan, Commission Vice President Valdis Dombrovskis said on Friday.

The Commission will present various options for further institutional development of the euro zone by the end of May. The euro zone budget is to be called a "fiscal stabilisation function."

"We are now working on a paper on completing the Economic and Monetary Union (EMU) by the end of May, with more institutional aspects, including a euro area fiscal stabilisation function," Dombrovskis told Reuters.

Speaking on the sidelines of the annual meetings of the International Monetary Fund and World Bank in Washington, he said the details of how the budget would be financed, who would be in charge of it and how big it would be were yet to be discussed.

"We are assessing different models, but respecting conditions ... like the one that it should not result in permanent transfers among euro zone member states and not create moral hazard," he said.

The budget's investment support function could be modelled on the existing European Fund for Strategic Investment (EFSI), which encourages private investment in infrastructure, research and development and energy sectors by covering the more risky parts of projects through the leveraging of public funds.

Dombrovskis said setting up the unemployment re-insurance scheme would be politically more difficult and require some prior convergence of euro zone labour market institutions.

The scheme would likely employ a claw-back principle, where budget funds spent on supporting unemployment spending in countries hit by asymmetric shocks would have to be repaid when the business cycle turns.

"The ambition is not to set out all the details, but to outline the direction of work and if there is agreement on the direction, then we can work on the details," Dombrovskis said.

"It is no secret there are very different signals from different member states on this," he said.

Under the plan of further euro zone integration, the new institutional setup should be ready by 2025, Dombrovskis said.

The European Union of all 28 countries already has a budget, equal to around 1 percent of Gross National Income of the EU, or around 145 billion euros, spent mainly on supporting agriculture and the development of the bloc's poorer regions.